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less than 0.1. The equation for f is \frac{1}{f^{1 / 2}}=2 \log _{10}\left(\operatorname{Re} f^{1 / 2}\right)-0.8 where Re is a constant, termed the Reynolds number, which varies with the fluid properties, flow rate, and tube diameter. Obtain the approximate value of the friction factor by the search method, and then use the Newton-Raphson method to converge to the root for Re = 104 and 106.

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